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A087086 Primitive sets of integers, each subset mapped onto a unique binary integer, values here shown in decimal. 2
0, 1, 2, 4, 6, 8, 12, 16, 18, 20, 22, 24, 28, 32, 40, 48, 56, 64, 66, 68, 70, 72, 76, 80, 82, 84, 86, 88, 92, 96, 104, 112, 120, 128, 132, 144, 148, 160, 176, 192, 196, 208, 212, 224, 240, 256, 258, 264, 272, 274, 280, 288, 296, 304, 312, 320, 322, 328, 336, 338, 344 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A primitive set of integers has no pair of elements one of which divides the other. Each element i in a subset contributes 2^(i-1) to the binary value for that subset. The integers missing from the sequence correspond to nonprimitive subsets.

REFERENCES

Alan Sutcliffe, Divisors and Common Factors in Sets of Integers, awaiting publication

LINKS

Table of n, a(n) for n=0..60.

EXAMPLE

a(10)=22 since the 10th primitive set counting from 0 is {5,3,2}, which maps onto 10110 binary = 22 decimal.

From Gus Wiseman, Oct 31 2019: (Start)

The sequence of terms together with their binary expansions and binary indices begins:

   0:       0 ~ {}

   1:       1 ~ {1}

   2:      10 ~ {2}

   4:     100 ~ {3}

   6:     110 ~ {2,3}

   8:    1000 ~ {4}

  12:    1100 ~ {3,4}

  16:   10000 ~ {5}

  18:   10010 ~ {2,5}

  20:   10100 ~ {3,5}

  22:   10110 ~ {2,3,5}

  24:   11000 ~ {4,5}

  28:   11100 ~ {3,4,5}

(End)

MATHEMATICA

stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}];

Select[Range[0, 100], stableQ[Join@@Position[Reverse[IntegerDigits[#, 2]], 1], Divisible]&] (* Gus Wiseman, Oct 31 2019 *)

CROSSREFS

A051026 gives the number of primitive subsets of the integers 1 to n.

The version for prime indices (rather than binary indices) is A316476.

The relatively prime case is A328671.

Partitions with no consecutive divisible parts are A328171.

Compositions without consecutive divisible parts are A328460.

A ranking of antichains is A326704.

Cf. A000120, A048793, A070939, A285572, A285573, A303362, A304713, A305148, A328593.

Sequence in context: A090404 A015937 A058825 * A301587 A319796 A103288

Adjacent sequences:  A087083 A087084 A087085 * A087087 A087088 A087089

KEYWORD

easy,nonn,base

AUTHOR

Alan Sutcliffe (alansut(AT)ntlworld.com), Aug 14 2003

STATUS

approved

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Last modified December 5 20:45 EST 2019. Contains 329779 sequences. (Running on oeis4.)